Mass transport studies at rotating cylinder electrode during zinc removal from dilute solutions

The mass transport in the rotating cylinder electrode (RCE) for the Zn(II) recovery from dilute solutions was investigated. Global mass transport data were obtained by monitoring the (first order) concentration decay of dissolved zinc in sulfate media at pH 2. The electrolyses were performed at holding potential of −1.7 V vs. sat. MSE at Reynolds numbers comprised between 15 470 ≤ Re ≤ 123 680. Based on the analysis of Sh = aRe^bSc^0.356 correlation, the value of the constant a, associated with shape and cell dimensions, was 0.65; while the constant b, associated with hydrodynamic regime, exhibits a value of 0.48, which obeys to smooth zinc deposits on RCE interface. The mass transport in the Zn(II)/Zn cathode interface process differs with other deposition process, which usually gives roughness deposits.     

Rotating cylinder Hull cell study of anomalous codeposition of binary iron-group alloys

The anomalous codeposition of the iron group metals was investigated using the rotating cylinder Hull (RCH) cell. Single metals and binary alloys of iron, nickel and cobalt were deposited in the RCH cell and the partial current densities were determined as a function of length by position sensitive X-ray fluorescence analysis. The measured overall polarization behaviour was used as a boundary condition for the numerical calculation of the potential distribution along the cylinder using the Laplace equation. By combining the results the partial current density potential curves were established. Experiments performed at different rotation rates confirmed the inhibiting effect of the less noble metal on the deposition of the more noble metal. The inhibiting effect of iron on nickel disappeared when iron reached the limiting current. Strong evidence was found that in binary alloy deposition of iron, cobalt and nickel the reaction rate of the less noble metal is promoted by the presence of the more noble component.     

A primary, secondary and pseudo-tertiary mathematical model of a chlor-alkali membrane cell

A theoretical study of current density and potential at the anode, membrane and cathode, of a chlor-alkali membrane cell where the electrode blades are placed vertically, is presented. A representative unit cell is modelled in primary, secondary and pseudo-tertiary current distribution models. It is shown that electrolyte and membrane resistance has the greatest effect on current distribution. Furthermore, it is shown that there is a surprisingly small influence of mass transport on current distribution, on the assumption that the diffusion layer is of constant thickness. In converse to this, it is shown that mass transport affects the anode overpotential distribution to the extent that conclusions can be made about the occurrence of side-reactions and where they occur. Finally, it is shown that it is possible to estimate tertiary behaviour with a secondary current distribution model, by using an analytic expression at the anode surface.     

Determination of mass diffusion overpotential distribution with flow pulse method from current distribution measurements in a PEMFC

The mass diffusion overpotential distribution in a free-breathing proton exchange membrane fuel cell (PEMFC) was determined from current distribution measurements using a flow pulse approach. The current distribution measurements were conducted with a segmented flow-field plate. Flow pulses were fed to the cathode channels to form a uniform oxygen concentration distribution along the channels. Simultaneously, the cell resistance was monitored using the current interruption method. From the experimental data, the mass diffusion overpotential distribution was calculated using the Tafel equation. The results show that the mass diffusion overpotential in different parts of the cell may vary considerably, for example, at 180 mA cm^–2 the mass diffusion overpotential difference between the bottom and top part of the cell was 0.1 V.     

Three-dimensional numerical simulation of straight channel PEM fuel cells

The need to model three-dimensional flow in polymer electrolyte membrane (PEM) fuel cells is discussed by developing an integrated flow and current density model to predict current density distributions in two dimensions on the membrane in a straight channel PEM fuel cell. The geometrical model includes diffusion layers on both the anode and cathode sides and the numerical model solves the same primary flow related variables in the main flow channel and the diffusion layer. A control volume approach is used and source terms for transport equations are presented to facilitate their incorporation in commercial flow solvers. Predictions reveal that the inclusion of a diffusion layer creates a lower and more uniform current density compared to cases without diffusion layers. The results also show that the membrane thickness and cell voltage have a significant effect on the axial distribution of the current density and net rate of water transport. The predictions of the water transport between cathode and anode across the width of the flow channel show the delicate balance of diffusion and electroosmosis and their effect on the current distribution along channel.     

Mass transport studies at rotating cylinder electrode: Influence of the inter-electrode gap

This study shows the effect of using two different inter-electrode gaps on the RCE mass transport characterization. The average mass transport coefficient was calculated using the limiting current technique, using the soluble reduction of triiodide (smooth RCE interface) and the copper deposition (roughness RCE interface) in KNO₃ and H₂SO₄, respectively. Based on the analysis of the Sh = aRe^bSc^0.356 correlation, the values of the constant a, associated with shape and cell dimensions, were 0.89 and 3.8, in the soluble system (I₃⁻/I⁻), for the gaps of 2.4 and 3.2 cm, respectively, indicating that this coefficient increases with inter-electrode space. While for copper deposition, these values were 0.00081 and 0.014, for the gaps of 2.4 and 3.2 cm. The constant b, associated with hydrodynamic regime, exhibits values of 0.43 and 0.33 for the gaps of 2.4 and 3.2 cm, respectively, in the system I₃⁻/I⁻, indicating that hydrodynamics on the smooth RCE diminishes according to the inter-electrode space. While for the system (Cu(II)/Cu), the values of b were 0.91 and 0.88, for the gaps of 2.4 and 3.2 cm. These values were higher for the copper deposition than for the soluble system, due to microturbulence at the roughened (and often powdery deposits) RCE interface. From the analysis performed in this paper is clear that inter-electrode gap and hydrodynamics on the smooth and roughness RCE interface (given by the nature of reduction reaction) modify the mass transport correlation.     

A Two‐Phase Non‐Isothermal PEFC Model: Theory and Validation

A two‐dimensional, non‐isothermal, two‐phase model of a polymer electrolyte fuel cell (PEFC) is presented. The model is developed for conditions where variations in the streamwise direction are negligible. In addition, experiments were conducted with a segmented cell comprised of net flow fields. The, experimentally obtained, current distributions were used to validate the PEFC model developed. The PEFC model includes species transport and the phase change of water, coupled with conservation of momentum and mass, in the porous backing of the cathode, and conservation of charge and heat throughout the fuel cell. The current density in the active layer at the cathode is modelled with an agglomerate model, and the contact resistance for heat transfer over the material boundaries is taken into account. Good agreement was obtained between the modelled and experimental polarization curves. A temperature difference of 6 °C between the bipolar plate and active layer on the cathode, and a liquid saturation of 6% at the active layer in the cathode were observed at 1 A cm^–2.     

Modeling of transport, chemical and electrochemical phenomena in a cathode-supported SOFC

This paper investigates the performance of a planar cathode-supported solid oxide fuel cell (SOFC) with composite electrodes using a detailed numerical model. The methane reforming reaction is included in the model and takes place mostly in the porous, thin anode at the high operating temperature of 800-1000^°C. A single computational domain comprises the fuel and air channels and the electrodes-electrolyte assembly eliminating the need for internal boundary conditions. The equations governing transport and chemical and electrochemical processes for mass, momentum, chemical and charged species and energy are solved using Star-CD augmented by subroutines written in-house. The operating cell voltage is determined by the potential difference between the cathode and the anode, whose potentials are fixed. Results of temperature, chemical species, current density and electric potential distribution for a co-flow configuration are shown and discussed. It is found that the sub-cooling effect observed in anode-supported cells is almost ameliorated, making the cathode-supported cell favorable from the viewpoint of material stability.     

A three-dimensional numerical simulation of the transport phenomena in the cathodic side of a PEMFC

A three-dimensional numerical model is developed to simulate the transport phenomena on the cathodic side of a polymer electrolyte membrane fuel cell (PEMFC) that is in contact with parallel and interdigitated gas distributors. The computational domain consists of a flow channel together with a gas diffusion layer on the cathode of a PEMFC. The effective diffusivities according to the Bruggman correlation and Darcy's law for porous media are used for the gas diffusion layer. In addition, the Tafel equation is used to describe the oxygen reduction reaction (ORR) on the catalyst layer surface. Three-dimensional transport equations for the channel flow and the gas diffusion layer are solved numerically using a finite-volume-based numerical technique. The nature of the multi-dimensional transport in the cathode side of a PEMFC is illustrated by the fluid flow, mass fraction and current density distribution. The interdigitated gas distributor gives a higher average current density on the catalyst layer surface than that with the parallel gas distributor under the same mass flow rate and cathode overpotential. Moreover, the limiting current density increased by 40% by using the interdigitated flow field design instead of the parallel one.     

Modelling Approach for Planar Self‐Breathing PEMFC and Comparison with Experimental Results

This paper presents a model‐based analysis of a proton exchange membrane fuel cell (PEMFC) with a planar design as the power supply for portable applications. The cell is operated with hydrogen and consists of an open cathode side allowing for passive, self‐breathing, operation. This planar fuel cell is fabricated using printed circuit board (PCB) technology. Long‐term stability of this type of fuel cell has been demonstrated. A stationary, two‐dimensional, isothermal, mathematical model of the planar fuel cell is developed. Fickian diffusion of the gaseous components (O₂, H₂, H₂O) in the gas diffusion layers and the catalyst layers is accounted for. The transport of water is considered in the gaseous phase only. The electrochemical reactions are described by the Tafel equation. The potential and current balance equations are solved separately for protons and electrons. The resulting system of partial differential equations is solved by a finite element method using FEMLAB (COMSOL Inc.) software. Three different cathode opening ratios are realized and the corresponding polarization curves are measured. The measurements are compared to numerical simulation results. The model reproduces the shape of the measured polarization curves and comparable limiting current density values, due to mass transport limitation, are obtained. The simulated distribution of gaseous water shows that an increase of the water concentration under the rib occurs. It is concluded that liquid water may condense under the rib leading to a reduction of the open pore space accessible for gas transport. Thus, a broad rib not only hinders the oxygen supply itself, but may also cause additional mass transport problems due to the condensation of water.     

Experimental investigation of the primary and secondary current distribution in a rotating cylinder Hull cell

A rotating cylinder cell having a nonuniform current distribution similar to the traditional Hull cell is presented. The rotating cylinder Hull (RCH) cell consists of an inner cylinder electrode coaxial with a stationary outer insulating tube. Due to its well-defined, uniform mass-transfer distribution, whose magnitude can be easily varied, this cell can be used to study processes involving current distribution and mass-transfer effects simultaneously. Primary and secondary current distributions along the rotating electrode have been calculated and experimentally verified by depositing copper.List of symbols c distance between the cathode and the insulating tube (cm) - F Faraday's constant (96 484.6 C mol^–1) - h cathode length (cm) - i local current density (A cm^–2) - i _L limiting current density (A cm^–2) - i _ave average current density along the cathode (A cm^–2) - i ₀ exchange current density (A cm^–2) - I total current (A) - M atomic weight of copper (63.54 g mol^–1) - n valence - r _p polarization resistance () - t deposition time (s) - V _c cathode potential (V) - Wa _T Wagner number for a Tafel kinetic approximation - x/h dimensionless distance along the cathode surface - z atomic number Greek symbols _a anodic Tafel constant (V) - _c cathodic Tafel constant (V) - solution potential (V) - overpotential at the cathode surface (V) - density of copper (8.86 g cm^–3) - electrolyte conductivity ( cm^–1) - deposit thickness (cm) - _ave average deposit thickness (cm) - surface normal (cm)     

A study of current distribution in a DEM cell during bromate formation

The anodic oxidation of potassium bromide to potassium bromate is performed in an undivided cell with hydrogen evolution the major reaction at the counter electrode. The cell used is a dished electrode membrane (DEM) cell. Current density distribution, measured using a segmented electrode, shows a variation in the two principle dimensions; along the length of the electrode and over the width of the electrode. Current densities are highest at the electrolyte flow inlet and also exhibit a localized maximum along the electrode length. The variation in current density is due to the influence of electrolytic gas evolution on the effective electrolyte conductivity and mass transport and also due to the change in shape of the dished electrode, which influences mass transport, electrical potential field and flow at the cell inlet and exit.     

Large-scale simulation of polymer electrolyte fuel cells by parallel computing

A three-dimensional, electrochemical-transport fully coupled numerical model of polymer electrolyte fuel cells (PEFC) is introduced. A complete set of conservation equations of mass, momentum, species, and charge are numerically solved with proper account of electrochemical kinetics and water management. Such a multi-physics model combined with the need for a large numerical mesh results in very intense computations that require parallel computing in order to reduce simulation time. In this study, we explore a massively parallel computational methodology for PEFC modeling, for the first time. The physical model is validated against experimental data under both fully and low-humidified feed conditions. Detailed results of hydrogen, oxygen, water, and current distributions in a PEFC of 5-channel serpentine flow-field are discussed. Under the fully humidified condition, current distribution is determined by the oxygen concentration distribution. Cell performance decreases in low-humidity inlet conditions, but good cell performance can still be achieved with proper water management. Under low-humidity conditions, current distribution is dominated by the water distribution at high cell voltages. When the cell voltage is low, the local current density initially increases along the flow path as the water concentration rises, but then starts to decrease due to oxygen consumption. Under both fully and low-humidified conditions, numerical results reveal that the ohmic losses due to proton transport in anode and cathode catalyst layers are comparable to that in the membrane, indicating that the catalyst layers cannot be neglected in PEFC modeling.     

Experimental study on the effect of reactant flow arrangements on the current distribution in proton exchange membrane fuel cells

Current distribution in a proton exchange membrane fuel cell (PEMFC) is significantly influenced by reactant flow configurations. In this study, the current distribution has been measured experimentally using a segmented flow-field plate and printed circuit board (PCB). Local current distributions for a PEMFC with serpentine flow field and three different flow arrangements including co-flow, cross-flow, and counter-flow arrangements for the anode and cathode streams are investigated along with the effect of flow channel orientation. It is shown that the counter-flow arrangement yields most uniform distribution for the current density, whereas the co-flow arrangement results in a considerable variation in the current density from the reactant gas stream inlet to exit. Flow channel orientation can also impact the cell performance and the current distribution appreciably. The limiting hydrogen concentration at the anode side due to the low stoichiometry condition can have a predominant effect on the current distribution and cell performance.     

Enhanced mass transport to a reticulated vitreous carbon rotating cylinder electrode using jet flow

The mass transport characteristics of a porous, rotating cylinder electrode (RCE, 1.0 cm diameter; 0.5, 0.9 or 1.2 cm long; 1.25, 2.25, 3.00 cm³ overall volume; 250-2000 rpm speed) fabricated from reticulated vitreous carbon (RVC, 60 ppi or 100 ppi) were investigated. The deposition of copper from an acid sulfate electrolyte (typically, deoxygenated 1 mM CuSO₄ in pH 2, 0.5 M Na₂SO₄ at 298 K) was used as a test reaction. The effect of a jet flow of electrolyte towards the electrode and the introduction of polypropylene baffles in the electrochemical cell were studied at controlled rotation rates of the RCE. The product of mass transport coefficient and volumetric electrode area (k_mA_e) is related to the rotation speed of the electrode. For the 60 ppi RVC RCE, the jet electrolyte flow (3.5 cm³ s⁻¹) enhanced the mass transport rates by a factor of 1.46 at low rotation speeds; this factor was reduced to 1.08 at high rotation speeds. For a 100 ppi electrode, the enhanced mass transport decreased from 1.26 to 1.03 at low and high rotation rates, respectively. Under the experimental conditions, baffles showed little effect on the mass transport rates to the RVC RCE. Mass transport to jet flow at an RVC RCE is compared to other RCEs using dimensionless group correlation.     

Theoretical studies of displacement deposition of nickel into porous silicon with ultrahigh aspect ratio

A model is developed to address the uniformity of displacement deposition of nickel inside porous silicon with an ultrahigh aspect ratio as high as 200. The nickel distribution is treated as a current distribution issue as in electrodeposition. It is shown that the deposition distribution along the pore depth exhibits a strong dependence on a polarization parameter ξ. High values of ξ correspond to mass transport limitations and lead to non-uniform distributions, whereas small ξ values, representing interfacial reaction control, produce uniform distributions. Non-uniform deposition primarily occurs at an initial stage in which the reaction is dominated by mass transfer. As the deposition process continues, the deposition rate drops to a low value, and the deposition uniformity shifts from Ni²⁺ mass transport limitations to its interfacial reaction control, leading to uniform Ni²⁺ concentration and deposition rate distributions. It is predicted that the non-uniformity at the initial stage could be remedied by increasing the bulk concentration of the nickel ions and decreasing the plating bath pH. In addition, the uniformity of the deposition distribution can be significantly improved by introducing inhibiting additive coumarin to the plating solution.     

Electrochemical removal of cadmium from dilute aqueous solutions using a rotating cylinder electrode of wedge wire screens

Rates of mass transfer at rotating cylinder electrodes of wedge wire screens were studied by measuring the limiting current for the cathodic reduction of ferricyanide as test reaction. The experimental data are well correlated by an empirical expression between the Sherwood number and the Reynolds number, both in terms of the internal slot opening as characteristic length, and including two additional dimensionless parameters in order to characterize the geometry of the screens. The performance of an undivided electrochemical batch reactor with a rotating cylinder cathode of wedge wire screens was tested analyzing the cadmium removal from dilute solutions. The effect of cathodic applied potential and size of the screen is studied. Taking into account the residual cadmium concentration the best results were obtained for a cathode potential of −1.1 V vs. SCE at 700 rpm, where the cadmium concentration decreased from 54 to 0.9 mg l⁻¹ after 30 min of electrolysis with a specific energy consumption of 10.7 kWh kg⁻¹ and a normalized space velocity of 3.54 h⁻¹.     

Effect of hydrophobicity and pore geometry in cathode GDL on PEM fuel cell performance

The effect of hydrophobic and structural properties of a single/dual-layer cathode gas diffusion layer on mass transport in PEM fuel cells was studied using an analytical expression. The simulations indicated that liquid water transport at the cathode is controlled by the fraction of hydrophilic surface and the average pore diameter in the cathode gas diffusion layer. Deposition of a hydrophobic microporous layer reduces the average pore diameter in the macroporous substrate. It also increases the hydrophobic surface, which improves the mass transport of the reactant. The optimized hydrophobicity and pore geometry in a dual-layer cathode GDL leads to an effective water management, and enhances the oxygen diffusion kinetics.     

On the modeling of water transport in polymer electrolyte membrane fuel cells

Water management is a critical issue in polymer electrolyte membrane (PEM) fuel cells, and water transport through the membrane, catalyst layer and gas diffusion layer has significant impact on the cell performance and durability. In this study, the mechanism of water transport processes in PEM fuel cells has been analyzed through 3-D unsteady non-isothermal simulations, along with a comprehensive examination of various modeling approaches in literature. It is shown that the finite rates of sorption/desorption of water in membrane affect the cell current output and the cell response time. Water dissolved in the membrane should be taken as the proper mechanism of water formation in the cathode of practical PEM fuel cells. Capillary pressure and relative permeability have significant impact on the distribution of liquid water saturation and transport, implying a need for their determination under specific PEM fuel cell conditions.